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The main distinction is generally in terms of magnitude. temblors are generally lighter eathquakes that cause little to no damage. (See: temblor - Wiktionary.) On the other hand a terremoto is usally a more severe earthquake. As a rough approximation I'd say anything below a 6.5 on the Richter scale would probably be called a temblor, while anything stronger would be refered to as a terremoto.

A second distinction that is also important to note is that while terremoto specifically refers to earthquakes (e.g. shifting and vibrations that come from within the earth), a temblor could be any type of shaking (of the ground.)

For Example:

○ La explosión de la bomba fue tan fuerte que un temblor que duró más de 10 segundos resultó! => The explosion of the bomb was so strong, that a quake (of the earth) that lasted more than 10 seconds resulted.

X La explosión de la bomba fue tan fuerte que un terremoto que duró más de 10 segundos resultó! => The explosion of the bomb was so strong, that a (seismic) quake that lasted more than 10 seconds resulted.

The second sentence in the above example sounds a bit awkward (but it might be acceptable depending on regional usage.)